We consider fourth order accurate compact schemes, in both space and time, for the second
order wave equation with a variable speed of sound. We demonstrate that usually this is …

Numerical approximations and modeling of many physical, biological, and biomedical
problems often deal with equations with highly varying coefficients, heterogeneous models …

In this paper, the difference potentials method-based ADI finite difference scheme is
proposed for numerical solutions of two-dimensional nonlinear convection–diffusion …

We solve the wave equation with variable wave speed on nonconforming domains with
fourth order accuracy in both space and time. This is accomplished using an implicit finite …

In this paper, we develop pollution-free finite difference schemes for solving the non-
homogeneous Helmholtz equation in one dimension. A family of high-order algorithms is …

Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to
solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal …

The method of difference potentials generalizes the method of Calderon's operators from
PDEs to arbitrary difference equations and systems. It offers several key advantages, such …

Highly-accurate numerical methods that can efficiently handle problems with interfaces
and/or problems in domains with complex geometry are crucial for the resolution of different …

Numerical approximations and computational modeling of problems from Biology and
Materials Science often deal with partial differential equations with varying coefficients and …

We present a robust and effective method for the numerical solution of the biharmonic
interface problem with discontinuities in both the solution and its derivatives. We use a …